Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 2: BEGINNER'S BOX - 2

A particle executing simple harmonic motion completes $1200$ oscillations per minute and passes through the mean position with a velocity of $3.14 {\mathrm{ms}}^{-1}$. Determine the maximum displacement of the particle from its mean position. Also obtain the displacement equation of the particle if its displacement be zero at the instant $t=0$.

A particle oscillates along the $x-$axis according to equation $x=0.05 \sin \left(5t-\frac{\pi }{6}\right)$, where $x$ is in metre and $t$ is in second. Find its velocity at $t=0$ second.

A particle is executing SHM given by $x=A\sin \left(\pi t+\varphi \right)$. The initial displacement of particle is 1 cm and its velocity is $\mathrm{\pi } \mathrm{cm} {\sec }^{-1}$ . Find the amplitude of motion and initial phase of the particle.

A body executing S.H.M. has its velocity, $10 \mathrm{cm} {\sec }^{-1}$ and, $7 \mathrm{cm} {\sec }^{-1}$ when its displacement from the mean position are, $3 \mathrm{cm}$ and, $4 \mathrm{cm},$ respectively. Calculate the length of the path.

A particle is executing S.H.M. of time period $4 \mathrm{s}$. What is the time taken by it to move from the 

(a) Mean position to half of the amplitude.

(b) Extreme position to half of the amplitude.

For a particle executing S.H.M. In which part of a complete oscillation

(a) Acceleration supports the velocity.

(b) Acceleration opposes the velocity.

The piston in the cylinder head of a locomotive has a stroke (twice of the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min., what is its maximum speed ?